As quantum computers are (very) far from computing the properties of cold, dense QCD [1]},
to proceed from first principles requires the functional renormalization group (FRG)
[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [6]}, [7]}, [8]}, [16]}, [17]}, [18]}, [19]}.
Ref. [9]} use a chiral effective model up to \(\sim 2 n_{\rm sat}\) ,
matching onto QCD perturbation theory with a Fierz complete FRG
[6]}, [7]}, [8]}
at intermediate \(n_B\) . They find evidence for a spike in the speed of sound
at \(\sim 10 n_{\rm sat}\)  [9]}, which is much higher than Ref. [25]}.
The ultimate goal is to use the parameters determined by the FRG in vacuum
[16]}, [17]}, [18]} to compute the EoS for nuclear matter.
Fu, Pawlowski, and Rennecke [19]} find that \(Z < 0\)  at rather high \(T\)  and \(\mu _B \ne 0\) ,
Fig. (21) of [19]}. A complete FRG analysis should certainly see a quantum pion liquid, if it exists.
